The theory of reversible computing is based upon composition of invertible primitives. In a conventional computer, the computation is logically organized around computing primitives, such as the NAND gate, which are non-invertible. Thus, when performing the AND operation, a certain amount of information about the system's past is generally erased. This loss of information or damping associated with an irreversible process must, according to the laws of physics, be accompanied by the thermalization of an about k.sub.B T of energy per bit. (See R. Landauer, Annals NY Acad. Sci. 426, 161 (1985); E. Fredkin and T. Toffoli, Int'l. J. Theor. Phys. 21, 219 (1982)). Interest in reversible computation thus arises from the desire to reduce heat dissipation in computing circuits, thereby allowing higher density and speed.
It appears possible in principle (See E. Fredkin and T. Toffoli, Intl. J. Theor. Phys. 21 (1982) 219; T. Toffoli, Seventh Colloq. Automata, Lang. and Prog., J. W. deBakker and J. van Leeuwen, eds., Springer, Berlin, (1980) 632; T. Toffoli, Math. Systsm. Th. 14 (1981) 13; and R. P. Feynman, Found. Phys. 16 (1986) 507) to design computing mechanisms which, if operated strictly in accordance with the laws of microphysics, dissipate zero free energy internally. Dissipation in such circuits would arise only in reading the output, which amounts to clearing the computer for further use. This total decoupling between the computational modes (due to signal interactions) and thermal modes is effectively achieved by reversing the computation after the results have been computed, restoring the circuit to its initial configuration.
In today's electronic semiconductor computers, the interaction of signals and signal damping/regeneration processes are usually inextricably intertwined within the same physical device (e.g. transistor), and are thus inseparable. Even if reversible gates were employed virtually every primitive computational step would involve unavoidable damping and regeneration of signals, with resultant dramatic heat loss. However, in other technologies--such as optical or superconducting systems--the decoupling between mechanical interaction modes and thermal ones can be effectively achieved. Such systems may, therefore, provide the way for a more natural correspondence between computation and fundamental principles of physics, leading to the realization of high-performance computing structures.
Optical implementation of various kinds of computing gates has been difficult in the past. In some cases, a gate can be implemented. (See B. S. Wherrett, Opt. Commun. 56 (1985) 87). But the output power from the gate is so low that cascading these gates into useful optical computing elements is impossible. Previously proposed implementations (See J. Shamir, H. Caulfield, W. Micelli, and R. Seymour, Appl. Opt. 25 (1986) 1605) of reversible computing gates suffer from additional problems. (See R. Cuykendall and D. McMillin, Appl. Opt. 26, (1987) 1959). In order for the gate to function as a completely reversible optical gate, no distinction can be made between the inputs. Each must be of the same type (in this case optical) and at the same level. Although gates not meeting the criteria described here have been shown useful for designing optical computing systems, (See R. Cuykendall and D. McMillin, Appl. Opt. 26, (1987) 1959), the unrestricted type of gate permits a significant reduction in circuit complexity.
An analysis of the nonlinear interface which assumes Gaussian beams of finite cross section and a nonlinear index of refraction proportional to the local intensity I(x,y) has been reported. (See W. J. Tomlinson, J. P. Gordon, P. W. Smith, and A. E. Kaplan, Appl. Opt. 21, 2041 (1982)). This analysis leads to significantly different predictions than the plane wave analysis of Kaplan, (See A. E. Kaplan, Sov. Phys. JEP 45, 896 (1977)). Specifically, a series of self-focussed channels in the nonlinear transmission region, the absence of hysteresis in the reflection coefficient, and a reflection coefficient which does not approach zero at some critical intensity (i.e., no transparentization of the interface) are predicted. However, the analysis assumes there is no diffusion of the nonlinear mechanism (free carriers, heat, or excited gas atoms). When diffusion is present, as in all real systems, an the diffusion length associated with the nonlinearity is of the order of or larger than the beam cross section, the nonlinear component to the index of refraction is approximately constant across the Gaussian beamwidth, precluding formation of self-focussed channels. Thus, the plane wave theory with its associated predictions of hysteresis and total transparentization of the interface for a critical intensity, more closely models real systems. Experimental results (See P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, Appl. Phys. Lett. 35, 846 (1979); P. W. Smith, W. J. Tomlinson, P. J. Maloney, and J. P. Hermann, J. Quant. Elect. QE-17, 340 (1981)) exhibit such hysteresis of the reflection coefficient supporting the plane wave approximation.